The Similarity Index to Decompose Two-Stage Stochastic Scheduling Problems

Abstract

Two-stage stochastic scheduling problems often involve a large number of continuous and discrete variables, so fnding solutions in short time periods is challenging and computationally expensive. However, for online or closed-loop scheduling implementations, optimal or near-optimal solutions are required in real-time. We propose a decomposition method based on the so-called Similarity Index (SI). An iterative procedure is set up so that each sub-problem (corresponding to a scenario) is solved independently, aiming to optimize the original cost function while maximizing the similarity of the frst-stage variables among the scenarios solutions. The SI is incorporated into each subproblem cost function, multiplied by a penalty parameter that is updated in each iteration until reaching complete similarity in the frst-stage variables among all subproblems. The method is applied to schedule production and maintenance tasks in an evaporation network. The tests show that signifcant benefts are expected in terms of computational demands as the number of scenarios increases.